Question

A rectangular vessel of base area, $320c{m}^2$ and height $11cm$ is full of kerosene oil. This kerosene is poured completely into a conical vessel. The top of the conical vessel has radius $10cm$. If the conical vessel is filled completely, determine its height.

Answer 1

Step 1: Find the volume of the rectangular vessel.

Given that, the base area of rectangular vessel is $320c{m}^2$ and its height $\left(h\right)$ is $11cm$

The volume of rectangular vessel $=areaofbase\times height$

$=320\times 11$

$=3520c{m}^3$

Step 2: Find the height of the conical vessel.

We have, volume of the rectangular vessel $=$ volume of the conical vessel.

Also, radius $\left(r\right)$ of the conical vessel $=10cm$

The volume of the cone having radius $\left(r\right)$ and height $\left(h\right)$ $=\frac{1}{3}{\mathrm{\pi r}}^2\mathrm{h}$

$\Rightarrow 3520=\frac{1}{3}\times \frac{22}{7}\times {\left(10\right)}^2\times h$ $\left(\mathrm{\pi }=\frac{22}{7}\right)$

$\Rightarrow 3520=\frac{1}{3}\times \frac{22}{7}\times 100\times h$

$\Rightarrow \frac{3520\times 3\times 7}{22\times 100}=h$

$\Rightarrow h=\frac{88\times 3\times 7}{11\times 5}$

$\Rightarrow h=33.6cm$

Hence, the height of the conical vessel is $33.6cm$.